Discuss the below problems:
Q1. Callaway Golf Company's new forged titanium ERC driver has been described as "illegal" because it promises driving distances that exceed the USGA's standard. Golf Digest compared actual driving distances with the ERC driver and a USGA approved driver with a population mean driving distance of 280 yards. Based on nine test drives, the mean driving distance by the ERC driver was 286.9 yards (Golf Digest, May 12, 2000). Answer the following questions assuming a sample standard deviation driving distance of 10 yards.
a. Formulate the null and alternate hypotheses that can be used to determine whether the new ERC driver has a population mean driving distance greater than 280 yards.
b. On average, how many yards farther did the golf ball travel with the ERC driver?
c. At α = 0.05, what is your conclusion?
Q2. Microsoft Outlook is the most widely used e-mail manager. A Microsoft executive claims that Microsoft Outlook is used by at least 75% of the Internet users. A sample of Internet users will be used to test this claim.
a. Formulate the hypotheses that can be used to test the claim.
b. A Merrill Lynch study reported that Microsoft Outlook is used by 72% of Internet users (CNBC, June 2000). Assume that the report was based on a sample size of 300 Internet users. What is the p-value?
c. At α = 0.05, should the executive's claim of at least 75% be rejected?
Q3. An extensive study of the cost of health care in the United States presented data showing that the mean spending per Medicare enrollee was $6883. To investigate differences across the country, a researcher took a sample of 40 Medicare enrollees in Indianapolis. For the Indianapolis sample, the mean 2003 Medicare spending was $5980 and the standard deviation was $2518.
a. State the hypothesis for deter ming whether the mean annual Medicare spending in Indianapolis is lower than the national mean.
b. Use the preceding sample results to compute the test statistic and the p value.
c. Use a=.05(level of significance). What is your conclusion?
d. Repeat the hypothesis test using the critical value approach.